Many scientific, industrial, military weapons systems, and aerospace applications require precise and accurate knowledge of the angular orientation of a shaft or other rotating object. Typically, this knowledge is provided by a rotary shaft angle encoder. Encoders of the highest practical precision are relative or incremental in nature, i.e. they resolve very small angular changes and keep track of accumulated change relative to some reference angle. In these encoders the angular information generally is lost if this reference angle becomes corrupted, e.g., through power interruption or upset by electromagnetic interference. There are also absolute encoders which provide angle information which is independent of any reference angle (except of course its own calibration, traceable to some standards maintenance organization such as NIST--formerly NBS). The absolute nature of these encoders is generally accompanied by only low to moderate angular sensitivity. Those which have the highest sensitivity are exorbitantly expensive ($30,000 to $100,000). Further, some of these encoders often achieve additional sensitivity by means of gear trains which are subject to hysteresis which limit accuracy and make angular determination indirect.